﻿using System;
using Algorithms.Numeric.Decomposition;
using Utilities.Extensions;

namespace Algorithms.Numeric.Pseudoinverse
{
    /// <summary>
    ///     The Moore–Penrose pseudo-inverse A+ of a matrix A,
    ///     is a general way to find the solution to the following system of linear equations:
    ///     ~b = A ~y. ~b e R^m; ~y e R^n; A e Rm×n.
    ///     There are varios methods for construction the pseudo-inverse.
    ///     This one is based on Singular Value Decomposition (SVD).
    /// </summary>
    public static class PseudoInverse
    {
        /// <summary>
        ///     Return the pseudoinverse of a matrix based on the Moore-Penrose Algorithm.
        ///     using Singular Value Decomposition (SVD).
        /// </summary>
        /// <param name="inMat">Input matrix to find its inverse to.</param>
        /// <returns>The inverse matrix approximation of the input matrix.</returns>
        public static double[,] PInv(double[,] inMat)
        {
            // To compute the SVD of the matrix to find Sigma.
            var (u, s, v) = ThinSvd.Decompose(inMat);

            // To take the reciprocal of each non-zero element on the diagonal.
            var len = s.Length;

            var sigma = new double[len];
            for (var i = 0; i < len; i++)
            {
                sigma[i] = Math.Abs(s[i]) < 0.0001 ? 0 : 1 / s[i];
            }

            // To construct a diagonal matrix based on the vector result.
            var diag = sigma.ToDiagonalMatrix();

            // To construct the pseudo-inverse using the computed information above.
            var matinv = u.Multiply(diag).Multiply(v.Transpose());

            // To Transpose the result matrix.
            return matinv.Transpose();
        }
    }
}
